# Angle Please

Weekly Problem 19 - 2017

In the figure, what is the value of x?

In the figure, what is the value of x?

## Problem

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If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

## Student Solutions

There are two different ways of calculating the angle $x$.

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The blue angle can be calculated since angles on a straight line add to $180^\circ$. This means it is $180^\circ - 100^\circ = 80^\circ$.

The orange angle can be calculated similarly, to be $180^\circ - 93^\circ = 87^\circ$.

The green angle can then be calculated since the angles in the top-left triangle add up to $180^\circ$. This is $180^\circ - 80^\circ - 58^\circ = 42^\circ$.

The green and red angles are opposite angles. This means that they are equal, so the red angle is also $42^\circ$.

Then, the angles in the left-hand triangle must add up to $180^\circ$, so $x^\circ = 180^\circ - 42^\circ - 87^\circ= 51^\circ$.

Image

The angles in the red and purple triangle must add up to $180^\circ$, so the green angle is $180^\circ - 58^\circ - 93^\circ = 29^\circ$.

Then, the angles in the blue triangle must also add up to $180^\circ$. Therefore, $x^\circ = 180^\circ - 29^\circ - 100^\circ = 51^\circ$.